Aircraft: SMALL TRANSPORT; LOW WING; 2 TURBOPROP ENG
Phase of flight: Descent
Anomaly: ATC Issue All Types; Conflict Airborne Conflict; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy

Just got relief briefing from previous controller working north arrival gates combined. The previous controller had taken handoff on Aircraft X; but the pilot had not checked in yet. I noticed that Aircraft X had 'WWW' in his scratchpad and an 'E' which typcially indicates an overflight heading westbound. However; the aircraft was heading east and I didn't have an overflight strip so I needed to figure out where the aircraft was going. The pilot checked in at 16;000 ft. and mentioned 'Atis Victor'. I yelled to Flight Data (FD) to get a full route on the aircraft. When FD brought the strip over I saw that the aircraft was landing at ZZZ. Meanwhile another aircraft was checking in on an arrival and after I gave the pilot a runway to expect the pilot was going on and on about how he was issued a late descent by Center and couldn't make the crossing restriction. I issued Aircraft X a 110 heading and 14;000 ft. It was my intent to keep the aircraft north of a cluster of gliders that were hovering around 14;000 to 15;500 ft. south east of where Aircraft X was. However; the pilot read back 140 heading and 11;000 ft. I missed the incorrect readback but noticed the pilot was turning way more than a 110 heading. Now was in conflict with the gliders. During this situation I was also trying to get the datablock updated to show the correct destination which I tried to Multi F J A - and it still would not allow me to update the datablock. I was focused on this and trying to get it updated so I could handoff the aircraft to the correct sector. I decided it was in the pilot's best interest to continue turning to the right so I issued a 170 heading. Unfortunately the gliders are all over the place and I couldn't predict what they were doing so now that heading looked bad and I was completely UNSURE of which way to turn Aircraft X. I instructed the pilot to 'stop descent' and he ended up seeing the glider and climbed back up. There were a lot of factors that went into this event that became a problem for me. Aircraft X was supposed to come in on an airway but the previous controller had approved direct ZZZZZ [fix;] direct ZZZ. If the controller had briefed me on that perhaps I wouldn't have been hustling to try and figure out where the aircraft was going and what he was doing and trying to update the data block. All of which proved distracting when I should've been more focused on a correct readback and keeping the aircraft AWAY from the cluster of gliders.When Center amends the aircraft's route this causes the datablock to now show 'overflight' instead of a lander. This automation issue has been frequent since METROPLEX was implemented and we shouldn't have to be dealing with this. When a new system is implemented the flaws and kinks in automation should've already been worked out. If there is a KNOWN issue with automation then the controllers should be BRIEFED on it. Neither of which has occurred. Turboprop aircraft shouldn't be coming in the same gate with jets; and if the aircraft would've been on the airway per the Letter of Agreement; then none of this would have happened. TRACON Controller reported they did not realize an aircraft read back the wrong instructions and then observed it fly into confliction with gliders.